Question: All of the 4th grade teachers and students from Santa Rita went on a field trip to an art museum. Tickets were $$7.50$ each for teachers and $$4.50$ each for students, and the group paid $$58.50$ in total. The next month, the same group visited a science museum where the tickets cost $$15.00$ each for teachers and $$10.00$ each for students, and the group paid $$125.00$ in total. Find the number of teachers and students on the field trips.
Let $x$ equal the number of teachers and $y$ equal the number of students. The system of equations is: ${7.5x+4.5y = 58.5}$ ${15x+10y = 125}$ Solve for $x$ and $y$ using elimination. Multiply the top equation by $-2$ ${-15x-9y = -117}$ ${15x+10y = 125}$ Add the top and bottom equations together. ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $ {7.5x+4.5y = 58.5}$ to find $x$ ${7.5x + 4.5}{(8)}{= 58.5}$ $7.5x+36 = 58.5$ $7.5x = 22.5$ $x = \dfrac{22.5}{7.5}$ ${x = 3}$ You can also plug ${y = 8}$ into $ {15x+10y = 125}$ and get the same answer for $x$ ${15x + 10}{(8)}{= 125}$ ${x = 3}$ There were $3$ teachers and $8$ students on the field trips.